We analyze the Uhlmann fidelity of a pair of n-mode Gaussian states of the quantum radiation field. This quantity is shown to be the product of an exponential function depending on the relative average displacement and a factor fully determined by the symplectic spectrum of the covariance matrix of a specific Gaussian state. However, it is difficult to handle our general formula unless the Gaussian states commute or at least one of them is pure. On the contrary, in the simplest cases n = 1 and n = 2, it leads to explicit analytic formulae. Our main result is a calculable expression of the fidelity of two arbitrary two-mode Gaussian states. This can be applied to build reliable measures of quantum correlations between modes in various branches of quantum physics.

We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.

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We give a description of the continuous-variable teleportation protocol in terms of the characteristic functions of the quantum states involved. The Braunstein-Kimble protocol is written for an unbalanced homodyne measurement and arbitrary input and resource states. We show that the output of the protocol is a superposition between the input one-mode field and a classical one induced by measurement and classical communication. We choose to describe the input state distortion through teleportation by the average photon number of the measurement-induced field. Only in the case of symmetric Gaussian resource states we find a relation between the optimal added noise and the minimal EPR correlations used to define inseparability.

We write the optimal pure-state decomposition of any two-mode Gaussian state and show that its entanglement of formation coincides with the Gaussian one. This enables us to develop an insightful approach of evaluating the exact entanglement of formation. Its additivity is finally proven.

The general properties of the Coulomb Green's function are presented, together with its available compact integral representations and discrete state expansions. These representations are most useful as they provide elegant and efficient ways to compute 'exact' values of high-order perturbative matrix elements in hydrogen. Such calculations are of interest as they represent accurate benchmark data for multiphoton transition probabilities. Recent applications involving the Coulomb Green's function for the Dirac equation are also reviewed.

We consider a single-mode radiation field initially in a displaced squeezed thermal state. The weak interaction of such a field with a heat bath of arbitrary temperature is shown to preserve the Gaussian form of the characteristic function. Accordingly, the study of the time development of the density operator reduces to our previous description [P. Marian and T. A. Marian, preceding paper, Phys. Rev. A 47, 4474 (1993)] of the initial quantum state. As examples, photon statistics and squeezing properties of the damped field are analyzed. Based on the close relation between field dissipation and photon detection, we derive simple analytic formulas for the counting distribution and its factorial moments. Nonclassical features of a displaced squeezed thermal state, such as oscillations of the photon-number distribution, survive in the counting process, provided that the quantum efficiency of the detector is high enough.